We propose a moving-boundary scenario to model the penetration of diffusants into rubbers. Immobilizing the moving boundary by using the well-known Landau transformation transforms the original governing equations into new equations posed in a fixed domain. We solve the transformed equations by the finite element method and investigate the parameter space by exploring the eventual effects of the choice of parameters on the overall diffusants penetration process. Numerical simulation results show that the computed penetration depths of the diffusant concentration are within the range of experimental measurements. We discuss numerical estimations of the expected large-time behavior of the penetration fronts. To have trust in the obtained simulation results, we perform the numerical analysis for our setting. Initially, we study semi-discrete finite element approximations of the corresponding weak solutions. We prove both a priori and a posteriori error estimates for the mass concentration of the diffusants, and respectively, for the a priori unknown position of the moving boundary. Finally, we present a fully discrete scheme for the numerical approximation of model equations. Our scheme is based on the Galerkin finite element method for the space discretization combined with the backward Euler method for time discretization. In addition to proving the existence and uniqueness of a solution to the fully discrete problem, we also derive a priori error estimates for the mass concentration of the diffusants, and respectively, for the position of the moving boundary that fit to our implementation in Python. Our numerical illustrations verify the obtained theoretical order of convergence in physical parameter regimes.

Master of Science / Department of Computing and Information Sciences / Daniel Andresen / This report considers a native Android application called “KSUSoy YieldCalc” that assists in yield estimation of soybean before harvest following conventional approach. Android is one of the most popular installed base of any mobile platform, powering many mobile devices in more than 190 countries for users of diverse economic backgrounds, making it more popular than iOS devices (Android developers n.d.).The project “KSUSoy YieldCalc” adopted the Android platform as its base to serve farmers, agronomists, and consultants and deliver performance to save time and enhance farmers’ their confidence. The native application uses “conventional approach” of estimation of yield for calculations and eliminates the need for having Internet connection to access, thereby increasing the application’s flexibility. The project utilized Android Software Development Kit (SDK) as its development platform with extensive Java and Extensible Markup Language (XML) coding. The Department of Agronomy at Kansas State University (KSU) tested the application with promising results. Dr. Ignacio Ciampitti of the Department of Agronomy at KSU currently demonstrates the application to farmers. User feedback has been very satisfactory to date.

Master of Science / Department of Statistics / Leigh W. Murray / The term retrospective power describes methods for estimating the true power of a test after data have been collected. These methods have been recommended by some authors when null hypothesis of a test cannot be rejected. This report uses simulations to study power as a construct of an observed effect, variance, sample size, and set level of significance under the balanced one-way analysis of variance model for normally distributed populations with constant variance. Retrospective power, as a construct of sample data, is not recommended when the null hypothesis of a test cannot be rejected. When the p-value of the test is large, estimates for true power tend to fall below the 0.80 level and width-minimized confidence limits for true power tend to be wide.

Ill-posed inverse problems have wide applications in many fields such as oceanography, signal processing, machine learning, biomedical imaging, remote sensing, geophysics, and others. In this dissertation, we address the problem of solving unstable operator equations with iteratively regularized Newton-type algorithms. Important practical questions such as selection of regularization parameters, construction of generating (filtering) functions based on a priori information available for different models, algorithms for stopping rules and error estimates are investigated with equal attention given to theoretical study and numerical experiments.

No description available.

MBA Professional Report / The purpose of this MBA Project is to review existing policy of the Federal Energy Management Program under the purview of National Renewal Energy Laboratory (NREL) for Energy Savings Performance Contracts (ESPCs). This project will assess the ability for the Department of Defense to incorporate emerging technologies in alternative energy to supplement or replace existing power sources for DoD installations within the current Energy Savings Performance Contract policy. To do this the project will review previous and existing Energy Savings Performance Contracts. Further, this project will conduct a cost-benefit analysis of conventional power versus emerging photovoltaic energy for the Army’s Fort Bliss in El Paso, TX. The project will also analyze energy demands based on a new force alignment at Fort Bliss in accordance with the recent Base Realignment and Closure (BRAC) findings. The project will review current Energy Performance Contract Policy and recommend changes to allow for the use of emerging alternative energy technologies.

This thesis focuses on a certain type of nonlinear parabolic partial differential equations, i.e. PME and FDE. Chapter 1 consists of a survey on results related to PME and FDE, and a short review on some works about deriving gradient estimates in probabilistic ways. In Chapter 2 we estimate gradient on space variables of solutions to the heat equation on Euclidean space. The main idea is to construct two semimartingales by letting the solution and its gradient running backward on the path space of a diffusion process. Estimates derived from decompositions of those two semimartingales are then combined to give rise to an upper bound on gradient that only involves the maximum of the initial data and time variable. In particular, it is independent of the dimension. In Chapter 3 we carry the idea in Chapter 2 onto the study of positive solutions to PME or FDE, and obtained a similar type of bound on |∇u| for local solutions to PME or FDE on Euclidean space. In existing literature there have always been constraints on m. By considering a more general form of transformation on u and introducing a family of equivalent measures on path space, we add more flexibility to our method. Thus our result is valid for a larger range of m. For global solutions, when m violates our constraint, we need two-sided bound on u to control |∇u|. In Chapter 4 we utilize maximum principle to derive Li-Yau type gradient estimate for PME on a compact Riemannian manifold with Ricci curvature bounded from below. Our result is able to yield a Harnack inequality possessing the right order in time variable when the lower bound of Ricci curvature is negative.

I consider a model for the control of criminality in cities. The model was developed during my REU at UCLA. The model is a system of partial differential equations that simulates the behavior of criminals and where they may accumulate, hot spots. I have proved a prior bounds for the partial differential equations in both one-dimensional and higher dimensional case, which proves the attractiveness and density of criminals in the given area will not be unlimitedly high. In addition, I have found some local bifurcation points in the model.

The success of screening experiments hinges on the effect sparsity assumption, which states that only a few of the factorial effects of interest actually have an impact on the system being investigated. The development of a screening methodology to harness this assumption requires careful consideration of the strengths and weaknesses of a proposed experimental design in addition to the ability of an analysis procedure to properly detect the major influences on the response. However, for the most part, screening designs and their complementing analysis procedures have been proposed separately in the literature without clear consideration of their ability to perform as a single screening methodology. As a contribution to this growing area of research, this dissertation investigates the pairing of non-replicated and partially–replicated two-level screening designs with model selection procedures that allow for the incorporation of a model-independent error estimate. Using simulation, we focus attention on the ability to screen out active effects from a first order with two-factor interactions model and the possible benefits of using partial replication as part of an overall screening methodology. We begin with a focus on single-criterion optimum designs and propose a new criterion to create partially replicated screening designs. We then extend the newly proposed criterion into a multi-criterion framework where estimation of the assumed model in addition to protection against model misspecification are considered. This is an important extension of the work since initial knowledge of the system under investigation is considered to be poor in the cases presented. A methodology to reduce a set of competing design choices is also investigated using visual inspection of plots meant to represent uncertainty in design criterion preferences. Because screening methods typically involve sequential experimentation, we present a final investigation into the screening process by presenting simulation results which incorporate a single follow-up phase of experimentation. In this concluding work we extend the newly proposed criterion to create optimal partially replicated follow-up designs. Methodologies are compared which use different methods of incorporating knowledge gathered from the initial screening phase into the follow-up phase of experimentation.

Antonín Hanuš 5. prosince 2014 This work deals with randomized clinical trials of medicaments. It examines three models of dependece of final values on initial values in case, that all variables are measured with some measurement error. For each model is derived effect of treatment estimate and its asymptotical properties, specifically consistency and asymptotical variance. The work mostly deals with linear model of analysis of covariance ANCOVA. The work fruther contents comparison of properties of estimates from all three models in case, that examined data come from a linear model. There is a comparison of asymptotical variances of estimates from all three models and for each of them there are examined conditions, when this model gives the best results. In the end there is a simulation study, which verifies all previous results. 1